@article {Bershtein2016,
	title = {Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants},
	journal = {Journal of High Energy Physics},
	volume = {2016},
	number = {7},
	year = {2016},
	month = {Jul},
	pages = {23},
	abstract = {<p>We provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.</p>},
	issn = {1029-8479},
	doi = {10.1007/JHEP07(2016)023},
	url = {https://doi.org/10.1007/JHEP07(2016)023},
	author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini}
}
